...
A measure of relative change in density
or molar volume under a unit pressure variation:| LaTeX Math Block |
|---|
| anchor | 1O0ADA |
|---|
| alignment | left |
|---|
|
\betaK = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right) = - \frac{1}{V_m} \left( \frac{\partial V_m}{\partial p} \right) |
| LaTeX Math Block |
|---|
|
\beta = \rho \cdot \left( \frac{\partial p}{\partial \rho} \right) = - V_m \cdot \left( \frac{\partial p}{\partial V_m} \right) |
It measures its Bulk modulus measures resistance of Continuum body to compression/decompression.to deformation and is inverse to compressibility :
| LaTeX Math Block |
|---|
|
K = \frac{1}{c} |
Bulk modulusCompressibility depends on the thermodynamic conditions at which it is measured and as such is not a material property.
The two major deformation processes of the medium compression/decompression processes are isothermal and isentropic which result in different values of compressibilityBulk modulus:
| Isothermal Compressibilitybulk modulus | Isentropic Compressibilitybulk modulus |
|---|
| |
| LaTeX Math Block |
|---|
| \betaK_T = \frac{1}{\rho}rho \cdot \left( \frac{\partial \rhop}{\partial p\rho} \right)_T |
| | LaTeX Math Block |
|---|
| \betaK_S = \frac{1}{\rho}rho \cdot \left( \frac{\partial \rhop}{\partial p\rho} \right)_S |
|
Both and are not dependent on the amount of chemical substance and defined under a clear specific conditions of thermodynamic process and as such are the material properties and properly tabulated for the vast majority of materials.
In engineering practise, when the term CompressibilityBulk modulus is used as material property it normally means Isothermal Compressibility: .Compressibility is related to Z-factor
and Formation Volume Factor (FVF) For isotropic materials it is related to Young modulus (E) and Poisson's ratio (ν) as:
...
...
...
...
...
| LaTeX Math Block |
|---|
|
\beta(p) = - \frac{1}{B} \frac{dB}{dp} |
...
...
...
...
On the other hand Petroleum Industry is traditionally using symbol to denote compressibility which often lead to confusion with heat capacity.
See also
...
Physics / Mechanics / Continuum mechanics / Continuum Body Continuum body/ Deformation
[ Solid Mechanics ] [ Fluid Mechanics]
[Compressibility] [ Young modulus (E) ][ Poisson's ratio (ν) ]
[ Isothermal Compressibility ][ Isentropic Compressibility ]
[Fluid compressibility] [Pore compressibility] [Total compressibility][ Compressibility (β or c)]
